What is ln(((x^2-5x+3)(x-5)^5)/((3x^2+2)^6)) ?

The solution to ln(((x^2-5x+3)(x-5)^5)/((3x^2+2)^6)) is ln(x^2-5x+3)+5ln(x-5)-6ln(3x^2+2)

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simplify ln(((x^2-5x+3)(x-5)^5)/((3x^2+2)^6))

simplify

ln (\frac{( x ^{2} - 5 x + 3 ) ( x - 5 ) ^{5}}{( 3 x ^{2} + 2 ) ^{6}})

ln (x^{2} - 5 x + 3) + 5 ln (x - 5) - 6 ln (3 x^{2} + 2)

Solution steps

ln (\frac{( x ^{2} - 5 x + 3 ) ( x - 5 ) ^{5}}{( 3 x ^{2} + 2 ) ^{6}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{( x ^{2} - 5 x + 3 ) ( x - 5 ) ^{5}}{( 3 x ^{2} + 2 ) ^{6}}) = ln ((x^{2} - 5 x + 3) (x - 5)^{5}) - ln ((3 x^{2} + 2)^{6})

= ln ((x^{2} - 5 x + 3) (x - 5)^{5}) - ln ((3 x^{2} + 2)^{6})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((3 x^{2} + 2)^{6}) = 6 ln (3 x^{2} + 2)

= ln ((x^{2} - 5 x + 3) (x - 5)^{5}) - 6 ln (3 x^{2} + 2)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln ((x^{2} - 5 x + 3) (x - 5)^{5}) = ln (x^{2} - 5 x + 3) + ln ((x - 5)^{5})

= ln (x^{2} - 5 x + 3) + ln ((x - 5)^{5}) - 6 ln (3 x^{2} + 2)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x - 5)^{5}) = 5 ln (x - 5)

= ln (x^{2} - 5 x + 3) + 5 ln (x - 5) - 6 ln (3 x^{2} + 2)

20 e^{9} + ln (12) + 50 + ln (9)

4 lo g_{10} (x) + 3 lo g_{10} (y) - 2 lo g_{10} (z)

3 ln (\frac{a}{2}) + 2 ln (2 b)

\frac{1}{2} ln (\frac{3}{4})

What is ln(((x^2-5x+3)(x-5)^5)/((3x^2+2)^6)) ?
The solution to ln(((x^2-5x+3)(x-5)^5)/((3x^2+2)^6)) is ln(x^2-5x+3)+5ln(x-5)-6ln(3x^2+2)